Waveguide gas laser with wavelength selective guide

ABSTRACT

A waveguide gas laser is disclosed wherein narrow resonances in the loss vs. wavelength characteristics of a hollow waveguide laser resonator are employed to achieve wavelength selectivity. The laser includes a capillary bore waveguide of radius a and length 2L (or length L in a half-symmetric arrangement) which contains a laser gas having a laser transition capable of providing stimulated emission of light at wavelength λ. The aforementioned loss resonances are achieved when the waveguide dimensions and the wavelength λ are of preselected values satisfying the relation ##EQU1## where N is a positive integer.

This invention relates to lasers, and more particularly relates to ahollow waveguide gas laser wherein the length of the waveguide isselected to provide low resonator loss for a particular laserwavelength.

Recently there has been considerable interest in waveguide gas laserswherein the laser light propagates through a hollow waveguide, typicallya capillary bore tube of dielectric material, which also serves toconfine the laser-exciting discharge. Waveguide gas lasers are describedby P. W. Smith, "A Waveguide Gas Laser," Applied Physics Letters, Vol.19 (Sept. 1, 1971), pages 132-134, by T. J. Bridges, E. G. Burkhardt andP. W. Smith, "CO₂ Waveguide Lasers," Applied Physics Letters, Vol. 20(May 15, l972), pages 403-405, and by R. L. Abrams and W. B. Bridges,"Characteristics of Sealed-Off Waveguide CO₂ Lasers," IEEE Journal ofQuantum Electronics, Vol. QE-9 (Sept. 1973), pages 940-946, and adetailed background analysis of light propagation modes in a hollowcircular waveguide is given by E. A. J. Marcatili and R. A. Schmeltzer,"Hollow Metallic and Dielectric Waveguides for Long Distance OpticalTransmission and Lasers," Bell System Technical Journal, Vol. 43 (July1964 ), pages 1783-1809.

Although waveguide gas lasers can achieve high gain in a small, compactdesign, the portion of the generated laser energy which appears insidelobes of the emitted laser beam is greater than that for other typesof lasers. Moreover, for lasers capable of operating on a number ofneighboring wavelength transitions, elements such as diffactiongratings, prisms, etalons, or other dispersive devices must be insertedinto the laser optical cavity in order to achieve laser line selection.This not only increases the complexity of the laser, but also introducesadditional loss in the laser cavity.

It is an object of the present invention to provide a waveguide gaslaser in which laser line selection is achieved by the waveguide itself,thereby eliminating the need for additional wavelength selectingelements.

It is a further object of the invention to provide a wavelengthselective hollow waveguide gas laser of simple and compact design, andwhich achieves minimum loss in the laser optical cavity.

It is a still further object of the invention to provide a waveguide gaslaser capable of generating a laser beam having a smaller percentage ofsidelobe energy than with waveguide gas lasers of the prior art.

A laser according to one embodiment of the invention includes awaveguiding member defining a capillary bore of radius a and length 2L.The capillary bore contains a laser gas having a laser transitioncapable of providing stimulated emission of light at wavelength λ. Thelaser gas is excited to invert the population of the energy levels ofthe laser transition, and an optical resonator is provided to reflectlight of wavelength λ back and forth through the capillary bore. Whenthe bore radius a and length 2L and the wavelength λ are of preselectedvalues satisfying the relation ##EQU2## where N is a positive integer,the laser operates at a waveguide resonance where significantly reducedloss is achieved. As a result, the waveguide itself functions toeffectively tune the laser to oscillate at the desired wavelength λ.

In another embodiment of the invention the capillary bore is of lengthL, and the optical resonator includes a reflector disposed sufficientlyproximate to an end of the waveguiding member that no appreciablediffraction occurs between the reflector and the adjacent end of thewaveguiding member. Reduced-loss waveguide resonances are achieved whenthe bore radius a and length L and the wavelength λ are of preselectedvalues satisfying the aforementioned relation

Additional objects, advantages and characteristic features of theinvention will be apparent from the following detailed description ofpreferred embodiments of the invention when considered in conjunctionwith the accompanying drawings wherein:

FIG. 1 is a partially schematic longitudinal sectional view illustratinga waveguide gas laser in accordance with one embodiment of theinvention;

FIG. 2 is a graph showing the resonator loss as a function of Fresnelnumber for the laser of FIG. 1;

FIG. 3 is a graph similar to FIG. 2 but with an expanded Fresnel numberscale to provide a more detailed illustration of a particular lossresonance; and

FIG. 4 is a partially schematic longitudinal sectional view illustratinga waveguide gas laser according to another embodiment of the invention.

Referring to FIG. 1 with greater particularity, a waveguide gas laser isshown including a tubular waveguiding member 10 defining a capillarybore 12 therethrough of radius a and length 2L. The waveguiding member10 may be of any material capable of guiding light at the wavelength ofinterest with negligible transmission loss. Typically, waveguidingmember 10 is of dielectric material such as BeO, Al₂ O₃ or fused SiO₂,although polished metal may also be employed, as long as sufficientlylow transmission loss is achieved at the wavelength of interest.

The capillary bore 12 is filled with a laser gas having a lasertransition capable of providing stimulated emission of light at adesired wavelength λ. As a specific example, the laser gas may be amixture of CO₂ and He operating on the P(20) 10.591 μm transition,although it should be understood that other laser gases and transitionsalso may be employed. For the aforementioned specific exemplary lasergas and transition, BeO is a good material for the waveguiding member 12on account of its negligible transmission loss in the vicinity of 10.591μm.

Hermetically sealed to the respective ends of the tubular waveguidingmember 10 and mounted in coaxial alignment with the tubular member 10are a pair of annular electrodes 14 and 16, of Kovar for example. Avoltage source 17 is connected between the electrodes 14 and 16 tosupply the appropriate operating voltage which establishes a dischargethrough the laser gas sufficient to invert the population of the energylevels of the desired laser transition. A pair of Brewster angle windows18 and 20, of CdTe for example, are attached by a suitable bonding agentsuch as epoxy to the outer ends of the respective electrodes 14 and 16.The assembly consisting of waveguiding member 10, electrodes 14 and 16,and Brewster windows 18 and 20 form a sealed enclosure for the laser gaswhich enables the desired gas pressure to be maintained. As a specificexample, when the laser gas is a mixture of CO₂ and He, with the ratioof He to CO₂ ranging from about 3:1 to about 14:1, the total gaspressure may range from about 50 Torr to about 300 Torr.

In order to provide an optical resonator for reflecting light ofwavelength λ back and forth through the capillary bore 12, a pair ofreflectors 22 and 24 are mounted beyond the respective Brewster anglewindows 18 and 20 a distance D from the respective ends of thewaveguiding member 10. Preferably, the reflectors 22 and 24 are concavemirrors having a radius of curvature R.

The coupling of light from the end of a waveguiding member such as 10 tothe free space between the waveguiding member and a curved mirror suchas 22 or 24 is discussed in detail by R. L. Abrams, "Coupling Losses inHollow Waveguide Laser Resonators," IEEE Journal of Quantum Electronics,Vol. QE-8 (November 1972), pages 838-843. For a waveguide bore radius a,there is an effective spot size of a Gaussian beam which best matchesthe waveguide given by

    w.sub.o = 0.6435a.                                         (1)

As discussed in the aforementioned paper by R. L. Abrams, the optimummirror curvature R is related to the mirror position D in accordancewith the relation

    R = D + B.sup.2 /D,                                        (2)

where B is a beam parameter defined as

    B = πw.sub.o.sup.2 /λ.                           (3)

In particular, Applicants have found that a mirror with a radius ofcurvature R = 2B positioned a distance D = B from the end of thewaveguide results in a resonator with low loss and very good transversemode selectivity (see R. L. Abrams and A. N. Chester, "Resonator Theoryfor Hollow Waveguide Lasers," Applied Optics, Vol. 13 (September 1974),pages 2117-2125). Thus, using Equations (1) and (3), appropriate valuesfor the mirror position D and radius of curvature R may be determinedfrom

    D = 1.3a.sup.2 /λ,                                  (4)

    R = 2.6a.sup.2 /λ.                                  (5)

The electric and magnetic field distributions and mode losses (couplingloss and guiding loss) for a hollow waveguide laser can be calculatedusing an iterative computational technique described by A. N. Chesterand R. L. Abrams, "Mode Losses in Hollow-Waveguide Lasers," AppliedPhysics Letters, Vol. 21 (Dec. 15, 1972), pages 576-578. Upon carryingout such a technique for a waveguide laser of the type described aboveand shown in FIG. 1, Applicants have discovered some unexpectedresonances in the laser resonator loss as a function of the waveguideFresnel number F_(N) = a² /λL, a dimensionless number characterizing thewaveguide. The round trip resonator loss as a function of Fresnel numberfor a waveguide laser according to FIG. 1 is shown by curve 30 of FIG.2. It may be seen from FIG. 2 that the resonator loss curve 30 has anumber of resonances 31, 32, 33 . . . 3N where significantly reducedloss is achieved. These loss resonances occur at respective Fresnelnumbers F_(N), where N is a positive integer, given by ##EQU4## Thus,resonance 31 occurs at F₁ = 0.125, resonance 32 at F₂ = 0.0625,resonance 33 at F₃ = 0.03125, etc.

Since a laser tends to operate in such a way as to favor the lowest losssituation, a laser having a narrow reduced-loss resonance in its lossvs. wavelength characteristic will tend to oscillate at the resonantwavelength. Thus, when a waveguide laser according to FIG. 1 isconstructed with the parameters a, 2L and λ selected to satisfy Equation(6), operation at one of the aforementioned reduced-loss resonances willoccur, thereby effectively tuning the laser so as to oscillate at thedesired wavelength λ.

Since the lowest order loss resonance 31 is spaced from the next lossresonance 32 by an amount greater than the spacing between any otherpair of adjacent resonances, it is preferred that the laser be designedto utilize the resonance 31, which may be achieved by selecting N = 1 inEquation (6). The loss resonance 31 at F₁ = 0.125 is illustrated in moredetail in FIG. 3. The width ΔF₁ of resonance 31 (measured where theamplitude of the resonance is halfway between its maximum and baselinevalues) is 7 × 10⁻ ⁴. This results in a wavelength resolution of Δλ/λ =5.6 × 10⁻ ³ which is slightly larger than the spacing between adjacentCO₂ laser transitions. The wavelength resolution also determines thetolerance to which the waveguide length must be machined, assuming thesquare of the waveguide radius is known to a similar tolerance.

As an illustrative example of a specific waveguide gas laser which maybe constructed in accordance with the invention, for a CO₂ laser mediumoperating at a wavelength of 10.591 μm, a waveguide bore radius of 0.5mm may be employed. Thus, solving Equation (6) with a = 0.5 mm, λ =10.591 μm and N = 1 gives a waveguide half-length L = 18.88 cm.Moreover, for these values of a and λ, Equations (4) and (5) give amirror separation D = 3.07 cm and radius of curvature R = 6.14 cm,respectively.

The theory underlying the aforementioned waveguide loss resonances canbe explained from the waveguide transmission characteristics. If thelaser is operating basically in a TEM_(oo) free space laser mode, asenergy is coupled from free space into the waveguide, several low orderwaveguide modes are excited. If these modes exit from the opposite endof the waveguide in phase (modulo 2π), they will exactly reconstruct theTEM_(oo) distribution in the free space outside of the opposite end ofthe waveguide, resulting in a low loss situation. Since 98% of theTEM_(oo) energy can be coupled to the lowest loss EH₁₁ waveguide mode(see the above-referenced article by R. L. Abrams, "Coupling Losses inHollow Waveguide Laser Resonators"), only a small amount of the energyis contained in the higher order waveguide modes.

In order to calculate the resonance condition, the phase shift for theEH_(nm) waveguide mode, for one transit, can be written as ##EQU5##where U_(nm) is the mth zero of the Bessel function of order (n - 1) andλ, L and a are as defined above. The Bessel function zeroes can beapproximated by

    U.sub.nm ≈ (m + n/2 - 1/4)π = (I/2 - 1/4)π   (8)

where I is a positive integer. The relative phase shift between any twomodes is given by ##EQU6## where P and Q are positive integers. For Δφ =2πJ where J is a positive integer, Equation (9) reduces to Equation (6),above, where N is a positive integer.

A further embodiment of the invention, employing a half-symmetric lasergeometry, is shown in FIG. 4. Components in the embodiment of FIG. 4which correspond to respective components in the embodiment of FIG. 1are designated by the same second and third reference numeral digits astheir counterpart components in FIG. 1, along with a prefix numeral "1".

The embodiment of FIG. 4 differs from that of FIG. 1 in that capillarybore 112 through waveguiding member 110 is of length L, and reflector124 has a flat reflective surface facing waveguiding member 110 anddisposed sufficiently proximate to the adjacent end of waveguidingmember 110 that no appreciable diffraction occurs between the end of thewaveguiding member 110 and reflector 124. This may be achieved when thedistance between reflector 124 and the adjacent end of waveguidingmember 110 is substantially less than 0.13a² /λ. Moreover, electrode 116consists of a metal rod having a cup-like portion 128 bonded to anenlarged portion of a countersunk radial bore 129 in member 110 in gasflow communication with capillary bore 112.

In the embodiment of FIG. 4 substantially all of the light travelingthrough capillary bore 112 and incident upon reflector 124 is reflectedback through capillary bore 112. Since this light travels through acapillary bore path of length 2L before exiting into free space, thearrangement of FIG. 4 is functionally equivalent to that of FIG. 1.Thus, in the embodiment of FIG. 4, reduced-loss resonances occur atrespective Fresnel numbers given by Equation (6), where L represents thelength of waveguiding member 110.

From the foregoing it may be seen that by constructing a waveguide lasersuch that the lasing wavelength and the waveguide radius and length areselected to satisfy Equation (6), the laser will operate at areduced-loss waveguide resonance. As a result, the waveguide itselffunctions to effectively tune the laser to the desired laser oscillationline, thereby eliminating the need for additional wavelength selectingelements. This enables the achievement of a wavelength selectivewaveguide gas laser of simple and compact design, and which is capableof generating a laser beam having a smaller percentage of sidelobeenergy than with waveguide gas lasers of the prior art.

Although the present invention has been shown and described withreference to particular embodiments, nevertheless various changes andmodifications which are obvious to a person skilled in the art to whichthe invention pertains are deemed to lie within the spirit, scope andcontemplation of the invention.

What is claimed is:
 1. A gas laser comprising:a waveguiding memberdefining a capillary bore of radius a and length 2L, a laser gasdisposed within said bore and having a laser transition capable ofproviding stimulated emission of light at wavelength λ, means inassociation with said waveguiding member for providing an enclosure forsaid laser gas, means for exciting said laser gas to invert thepopulation of the energy levels of said laser transition, opticalresonator means for reflecting light of wavelength λ back and forththrough said capillary bore; and said bore radius a and length 2L andsaid wavelength λ each being of a preselected value satisfying therelation ##EQU7## where N is a positive integer.
 2. A gas laseraccording to claim 1 wherein said optical resonator means includes apair of reflectors spaced from the respective ends of said waveguidingmember by a distance D given approximately by D = 1.3a² /λ.
 3. A gaslaser according to claim 2 wherein each of said reflectors has a concavereflective surface facing said waveguiding member and of a radius ofcurvature R given approximately by R = 2.6a² /λ.
 4. A gas laseraccording to claim 1 where N =
 1. 5. A gas laser comprising:awaveguiding member defining a capillary bore of radius a and length L, alaser gas disposed within said bore and having a laser transitioncapable of providing stimulated emission of light at wavelength λ, meansin association with said waveguiding member for providing an enclosurefor said laser gas, means for exciting said laser gas to invert thepopulation of the energy levels of said laser transition, opticalresonator means for reflecting light of wavelength λ back and forththrough said capillary bore, said optical resonator means including afirst reflector disposed sufficiently proximate to an end of saidwaveguiding member that no appreciable diffraction occurs between saidend of said waveguiding member and said first reflector, and said boreradius a and length L and said wavelength λ each being of a preselectedvalue satisfying the relation ##EQU8## where N is a positive integer. 6.A gas laser according to claim 5 wherein the distance between said firstreflector and said end of said waveguiding member is substantially lessthan 0.13a² /λ.
 7. A gas laser according to claim 6 wherein said opticalresonator means further includes a second reflector spaced from theopposite end of said waveguiding member by a distance D givenapproximately by D = 1.3a² /λ.
 8. A gas laser according to claim 7wherein said first reflector has a flat reflective surface facing saidwaveguiding member, and said second reflector has a concave reflectivesurface facing said waveguiding member and of a radius of curvature Rgiven approximately by R = 2.6a² /λ.
 9. A gas laser according to claim 5where N = 1.